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Journal ArticleDOI

From ultrasoft pseudopotentials to the projector augmented-wave method

15 Jan 1999-Physical Review B (American Physical Society)-Vol. 59, Iss: 3, pp 1758-1775
TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
Citations
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Journal ArticleDOI
19 Apr 2019-Science
TL;DR: Rare-earth doping is identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.
Abstract: High-performance piezoelectrics benefit transducers and sensors in a variety of electromechanical applications. The materials with the highest piezoelectric charge coefficients (d33) are relaxor-PbTiO3 crystals, which were discovered two decades ago. We successfully grew Sm-doped Pb(Mg1/3Nb2/3)O3-PbTiO3 (Sm-PMN-PT) single crystals with even higher d33 values ranging from 3400 to 4100 picocoulombs per newton, with variation below 20% over the as-grown crystal boule, exhibiting good property uniformity. We characterized the Sm-PMN-PT on the atomic scale with scanning transmission electron microscopy and made first-principles calculations to determine that the giant piezoelectric properties arise from the enhanced local structural heterogeneity introduced by Sm3+ dopants. Rare-earth doping is thus identified as a general strategy for introducing local structural heterogeneity in order to enhance the piezoelectricity of relaxor ferroelectric crystals.

442 citations

Journal ArticleDOI
TL;DR: The results show that, in order to prevent the deep-level defects from being effective recombination centers, the equilibrium carrier concentrations should be controlled so that the Fermi energy is about 0.3 eV away from the band edges.
Abstract: Inorganic–organic hybrid perovskites are a new family of solar cell materials, which have recently been used to make solar cells with efficiency approaching 20%. Here, we report the unique defect chemistry of the prototype material, CH3NH3PbI3, based on first-principles calculation. We found that both the Pb cations and I anions in this material exhibit strong covalency as characterized by the formation of Pb dimers and I trimers with strong covalent bonds at some of the intrinsic defects. The Pb dimers and I trimers are only stabilized in a particular charge state with significantly lowered energy, which leads to deep charge-state transition levels within the band gap, in contradiction to a recent proposal that this system has only shallow intrinsic defects. Our results show that, in order to prevent the deep-level defects from being effective recombination centers, the equilibrium carrier concentrations should be controlled so that the Fermi energy is about 0.3 eV away from the band edges. Beyond this r...

441 citations

Journal ArticleDOI
TL;DR: In this article, the thermodynamic properties of Al, Ni, NiAl, and Ni3Al were studied using the first-principles approach using the ab initio plane wave pseudopotential method within the generalized gradient approximation.

441 citations

Journal ArticleDOI
TL;DR: It is established that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes.
Abstract: The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

440 citations

References
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Book
31 Dec 1993
TL;DR: The linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged.
Abstract: With its extreme accuracy and reasonable computational efficiency, the linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. This volume presents a thorough and self-conta

1,150 citations